Problem 2
Question
Find the domain of each rational function. $$ f(x)=\frac{7 x}{x-8} $$
Step-by-Step Solution
Verified Answer
The domain of the function \(f(x) = \frac{7x}{x-8}\) is all real numbers except 8 or \((-\infty, 8) \cup (8, \infty)\) in interval notation.
1Step 1: Identify the denominator
In the function, \(f(x) = \frac{7x}{x-8} \), the denominator is \(x-8 \). The denominator is the part of the function we need pay special attention to in order to identify the domain of the function.
2Step 2: Set the denominator equal to zero and solve for x
To find what x-values should be excluded from the domain, we need to solve the equation where the denominator equals zero. So, we solve \(x-8 = 0\), this gives \(x = 8\).
3Step 3: Identify the domain
By knowing the x-value that makes the denominator zero, we can identify the domain of the function. The domain will include all real numbers except 8. In interval notation, this can be expressed as \((-\infty, 8) \cup (8, \infty)\).
Other exercises in this chapter
Problem 1
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$f(x)=x^{3}+x^{2}-4 x-4$$
View solution Problem 1
Determine which functions are polynomial functions. For those that are, identify the degree. \(f(x)=5 x^{2}+6 x^{3}\)
View solution Problem 2
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. \(y\) varies directly as \(x . y=45\) when \(x=5 .\) Find
View solution Problem 2
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=7 x^{2}+9 x^{4}$$
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